Geophysical Monograph Series Plasma Waves and Instabilities at Comets and in Magnetospheres Vol. 53 QUASINEUTRAL BEAM PROPAGATION IN SPACE

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1 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol. 53 QUASINEUTRAL BEAM PROPAGATION IN SPACE K. Ppdopoulos,* A. Mnkofsky nd A. Droot Science Applictions Interntionl Corportion, 171 Goodridge Drive, McLen, Virgini 1 Astrct. The propgtion of dense energetic neutrlized ion ems or plsmoids injected into plsm cross the mient mgnetic field under ionospheric conditions is considered. Using simple physicl model supported y two-dimensionl hyrid simultions, it is shown tht thin dense ems cn propgte llisticlly over lengths mny times their gyrordius. This occurs when the following conditions re stisfied: A/R < 1, where A is the cross field em width nd Ro the gyrordius of n mient ion hving velocity equl to the em velocity u, nd nm /no Mo >> 1, where n (M), no (Mo) re the density (mss) of em nd mient ions. The scling of the llistic propgtion lengths nd times with em nd mient prmeters is presented long with comments on the pplicility of the model to spce nd strophysics. Introduction The propgtion of high speed neutrlized ion ems, often clled plsmoids, cross mgnetic field is mong the oldest of prolems in plsm physics. It first rose in investigtions of the origin of mgnetospheric storms nd sustorms [Chpmn nd Ferrro, 1931; Ferrro, 195]. Despite the long history of investigtion, cler model hs yet to emerge. Erly theoreticl models estlished y Chpmn nd Ferrro [1931], Ferrro [195], Tuck [1959] nd Chpmn [196], indicted tht neutrlized em with lrge width A trnsverse to the mient mgnetic field B o (A R, where R is the gyrordius of the em ions), will in generl compress the mgnetic field ut will not propgte significntly. Propgtion cn potentilly occur in the dimgnetic regime when 47rnMq 1, where n, M, u re the den- * Permnent Address: Deprtment of Physics, University of Mrylnd, College Prk, Mrylnd 74. Copyright 1989 y the Americn Geophysicl Union. sity, mss nd cross field velocity of the em ions. This propgtion mode cn e properly descried y MHD nd is equivlent to the propgtion of solid conductor moving cross B o. During propgtion the em picks up nd crries long the mient plsm nd mgnetic field, in fshion similr to the pick-up of cometry ions y the solr wind [Crgill et l., 1988]. The mss loding, long with the vrious pick-up ring instilities, soon destroys the em coherence. Another propgtion mode proposed y Schmidt [196] ddressed the nrrow em regime, Re < A << R where Re is the electron gyrordius. This propgtion mode occurs in the nondimgnetic fi << 1 regime (often clled the electrosttic regime). In this cse the flow energy is not sufficient to lter the mgnetic field configurtion; therefore, the mient mgnetic field controls the electron nd ion dynmics. A polriztion electric field develops y the differentil motion of the mgnetized electrons (R, << A) nd the unmgnetized ions (R > A). The polriztion field E, coupled with the mient field B, llows the neutrlized em to move y n E x B o drift [Schmidt, 196]. This mode of propgtion ws experimentlly oserved y Bker nd Hmmel [1965]. Peter nd Rostoker [198] noted tht dielectric shielding due to the presence of n mient plsm does not ffect the em propgtion s long s VA p/va < 1, where Ku,,VAp re the em nd plsm Alfven speeds. Scholer's [197] model of rtificil propgtion of ion clouds in the mgnetosphere elongs to this clss of low kinetic 13, sulfvenic propgtion modes. In this pper we exmine plsmoid propgtion in the nrrow em regime discussed y Schmidt [196] ut for the high 13 (fl >> 1) strongly dimgnetic cse. It will e shown first y simple nlytic model, nd then y set of -D computer simultions using hyrid code [Mnkofsky et l., 1987], tht extremely long rnge propgtion cross the mgnetic field is possile in the strongly dimgnetic fi 1 regime if n no nd Re << A < u /1/ Ro, where fl o is the cyclotron frequency of the mient plsm ions. The propgtion physics nd the 149

2 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol QUASINEUTRAL BEAM PROPAGATION self-similr sttionry field configurtions re completely different from the high li MHD regime. Preliminry results on this propgtion mode ppered recently [Ppdopoulos et l., 1988]. In the MHD regime where the em width is much lrger thn the em ion gyrordius, R, we expect the ckground field to e excluded y ion dimgnetic effects. As consequence the ckground plsm nd mgnetic field will e swept y the em resulting in strong coupling t the em front. In the low 13 sitution descried y Schmidt where the em propgtes ecuse of the presence of polriztion electric field the interpenetrtion of the em y the ckground plsm is lso likely to led to strong coupling nd hence poor propgtion. However, for high f3 ion em which is nrrower thn its ion gyrordius, the possiility exists for diverting the ckground plsm nd mgnetic field symmetriclly round the em with minimum coupling or em-ckground interpenetrtion. In this sitution the high 13 ions hve sufficient energy to displce the ckground plsm t the em hed. Intuitively we expect the em front to erode t smll rte while the em ody remins undistured. Propgtion Model - Physicl Description Consider cold, dense (n >> no ), high kinetic et (fi 1) ion em intercting with n mient mgnetoplsm such s shown in Fig. 1. It is convenient to perform our nlysis in the em reference frme. In this frme for Bo = Bo ey, the mient mgnetized plsm flows with cross field velocity u o = u e,, with the id of motionl electric field E = (u, x B )/c = (u Bo)/c, where u o is the fluid velocity of the plsm electrons nd of the mgnetic flux. The equtions of motion of the ckground plsm ions (chrge e, mss Mo ) re dux = e uxbyl E dt Mo xc du x e[e, + u x By 1 dt Mo c (l) The vlue of the motionl electric field Ex (z) is given y E(z) u (z) x e B(z) u (z)b(z) = ex. () In the region z > hed of the em-plsm interfce (Fig. l), u o (z) =- u nd u o = u so tht the r.h.s. of (l) is zero. Nmely, the ions, the electrons nd the flux follow stright llistic orits. At the plsm interfce, Bo A ) BACKGROUND PLASMA,u = fszu l) Fig. 1. A schemtic of the physics involved during the interction of the ion em with the ckground plsm. z r:-.1, the fluid velocity uo reduces to no u u o (z) = no + n (z) to mintin chrge nd current neutrlity. This is ccompnied y dimgnetic current t the front nd field compression (Fig. l) such tht B(z)/B 1+n (z)/no. From Eq. (l) the reduction in u o (z) produces net force (eab(z)/mo c)u in the positive x-direction which diverts the plsm ions upwrds (Fig. l). In high )3 flow the electrons nd the flux follow the pth of the ions. For A < Ro chnge of the plsm frme speed u, (z) of the order of Due /u A/R is sufficient to estlish qusisttionry stte in which the ckground mgnetoplsm is diverted to one side of the em. In the lortory frme the ove interction corresponds to the em front diverting the mient plsm nd mgnetic field sidewys nd propgting freely. The em front suffers n erosion due to the energy required to divert the plsm sidewys. The resulting loss is, however, miniml for fi >> 1, llowing for long rnge em propgtion. An importnt ingredient of this propgtion mode is the highly symmetric stedy stte. This is contrry to the one expected y fluid or MHD models. It is dominted y kinetic ion effects. The vlidity of MHD models cn only e expected for scle lengths, A, lrger thn the em or ckground ion gyrordius. Furthermore, the MHD equtions which neglect ion inertil effects yield only symmetric solutions. A fluid tretment which includes ion inerti will llow symmetric solutions ut will miss the highly nonliner nd essentilly kinetic ion em ehvior t the em front. Notice tht in the electrosttic (or nondimgnetic) cse [Schmidt, 196] where AB nd Du e = flow diversion does not occur nd the em nd mient plsms will interpenetrte. Interpenetrtion cn cuse (3)

3 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol. 53 PAPADOPOULOS ET AL. 151 instilities tht destroy the coherence of the propgtion mode. Such em dispersl ws oserved in the lortory experiments of Birko nd Kirchenko [1978] in which n ion coustic wve ws driven unstle on the surfce of low-energy em in the /31, < 1 regime, pprently due to the reltive drift etween hevy nd light ions. Similr dispersl ws lso noted in -D prticle simultions of cross field ion em propgtion [Shnhn, 1984]. In this cse, the wve excittion ws ttriuted to the Bunemn instility. The excited surfce wve penetrted throughout the ulk of the plsm, ws ccompnied y strong electron heting nd resulted in dispersl of the em. In the next section we descrie representtive results from series of computer simultions which elucidte the physicl description presented ove, nd help clrify the resulting scling lws. Of utmost importnce in the study is the time over which the em propgtes llisticlly. The definition of llistic propgtion depends on the prticulr ppliction or mesurement resolution. For exmple, if one is concerned with sence of mgnetic effects, llistic propgtion will occur over time scle r such tht the lterl em displcement Az << R. For pplictions concerned with delivering the em energy flux t detector locted on llistic pth t distnce zo = u t, the criterion will e x /A < 1 t t = lu ( is the lterl em width). These issues re discussed in Section 5. Representtive Simultion Results Since the prolem is inhomogeneous, two-dimensionl, nd requires kinetic ion tretment, nlytic progress pst minor improvements on the ove simple nd intuitive picture is not possile. We therefore use numericl simultions. A two-dimensionl hyrid simultion code is the pproprite tool. The detils of the code pplied to the prolem cn e found in Mnkofsky et l. [1987]. Briefly, the ions re treted s discrete prticles, using stndrd prticle-in-cell techniques to follow their motion in the electromgnetic (EM) fields. Summing over the prticles provides the ion chrge nd current density. The electrons re treted s mssless fluid, descried vi the momentum nd energy equtions. These equtions, long with the ion equtions of motion, re solved self-consistently on uniform two-dimensionl grid for the ion velocity vectors, the EM fields, nd the electron pressure, in the nonrditive limit (i.e., Drwin Hmiltonin). The equtions solved in the simultion re: nd - c āt B -v x E V x B = 41r (J. + Ji ) The first eqution, Frdy's Lw, is used to determine the chnge in mgnetic field y inductive electric fields. In the second eqution, Ampere's Lw, the displcement current hs een neglected implying the condition V (J, + J,) =. This in conjunction with qusineutrlity, n. permits us to determine the velocity, u., of the electron fluid s function of mgnetic field nd ion current density. Further neglecting electron inerti, ut retining electron pressure nd collisionlity the electric field is found from force lnce for the electrons using generlized Ohm's Lw, uo V Po m. B ndel le[ E=--x ThEz (u _ u ) Po is the electron pressure determined from n pproprite electron energy eqution, nd v e, is the effective collision frequency with specie "s". The collision frequency cn e sed on clssicl Coulom interction or used to ccount for nonliner plsm coupling through the use of n nomlous prescription. The electric field contins oth n electrosttic s well s n inductive component. This model cn ccount for n extremely lrge rnge of physicl phenomen. It includes mipolr expnsion, mgnetic field convection, nd mgnetic field diffusion. The model resolves Alf<ren wves, whistlers, nd kinetic ion effects, nd ecuse it is explicit leds to the limittion r < O x, where At is the timestep, Az the smllest cell size, while V* is the mximum of the AlFren nd whistler wve phse velocities or the fstest ion velocity in prolem. The omission of electron inerti does not llow proper tretment of the electron skin depth so we limit our results to scle lengths much greter thn c/cope The system used in the ion em simultions hs periodic oundry conditions in the direction trnsverse to the flow (i.e., x-xis). In the flow direction (z-xis) plsm is injected from the right oundry t rte n o u nd permitted to leve on the left t the locl flux rte. The mgnetic field is llowed to flot t these oundries. We descrie elow simultion results designed to illustrte quntittively spects of the high # propgtion model. In the simultions presented here, the mient plsm ws composed of + with density no = 1 6 #/cm3 nd temperture.5 ev, nd ws emedded in mgnetic field Bo =.3 Guss. These re prmeters typicl of the ionospheric F-region. The em ws composed of protons nd ws given Gussin profile in the x nd z directions. Bem velocities u = 1 8, x 18 nd 4 x 1 8 cm/sec were studied, while the totl numer of em prticles vried

4 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol QUASINEUTRAL BEAM PROPAGATION S MIN. MAX. = 8. x 1 1 ff/cm 3 INC. = 8. x 13 N/CM 3 here were performed with the mgnetic field B o out of the plne of the simultion. (Runs were lso performed with the mgnetic field in the plne of the simultion. We will comment on these lter.) All the simultions were performed in the em reference frme. In this frme, the em prticles re initilly sttionry while the mgnetoplsm flows with u = -u ez, with the id of n pproprite motionl electric field. The geometry nd the initil conditions of the em in the simultions re shown in Figs. -c. Figure shows the em isodensity contours t t =. To fcilitte the understnding of the physics, dignostic cuts t the positions leled 1-5 were tken long the x nd z xes. Figures, c show the initil em profiles for cuts 1-5 long the x nd z xes. The physics of the interction descried in Section ecomes cler y referring to typicl simultion results. MIN. = MAX. = 8. x 1 1 ff/cm CUT LOCATIONS IN Z 11 3 CMI MIN = MAX. = 1. x 13 ff/cm : INC. = 1. x 11 ff/cm3 OIS 1, X -DIRECTION 113 CMI 9 MIN. - MAX. = 1.5 x 13 ff/cm 3 INC. = 1.5 x 1 1 ///CM Z DIRECTION 111 CMI Fig.. Initil em profiles for ll runs. The prmeters correspond to run #1. For the other runs they cn e scled ccording to the vlue of the pek em density n. () Bem isodensity contours. This figure shows lso the loctions of the verticl nd horizontl dignostic cuts in the x--z plne. () Bem density profiles long verticl cuts 1-5. (c) Bem density profiles long horizontl cuts Z-DIRECTION 11 3 CMI etween ", corresponding to pek em densities in the rnge of n Pe, 5 x 16-8 x 1 7 #/cm3. Tle Fig. 3. Isodensity em contours for run #1. () At I lists the prmeters of the simultion runs in rel (di- t = 1.5 msec or (equivlently fi t = 4 or propgtion mensionl) nd dimensionless units. The runs descried distnce 4R6 ). ()At t =.5 msec. 8 9

5 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol. 53 PAPADOPOULOS ET AL. 153 Run #1 of Tle I is exmined first. Computer time constrints limited the runs to times t <.5 msec, which corresponds to ilt PJ 8 or propgtion distnces of 8 R (fl = ebo lmc = 3 x 13 sec-1 is the proton cyclotron frequency). The evolution of the em for the prmeters of run #1 cn e seen from Figs. 3, nd 4,. Figures 3, show the em isodensity contours t times t = 1.5 nd.5 msec, corresponding to fl t = 4 nd 8 nd equivlent em propgtion distnces of 4 nd 8 R. It is cler tht the em hs mintined its mcroscopic integrity s plsmoid nd followed llistic trjectory. Similr conclusions re derived from Figs. 4,, which show the em profiles s function of x t the dignostic cuts. Figures 4, should e compred with Fig. t t =. Notice tht oth the isodensity contours nd the density profiles show density compression t the center of the em y lmost fctor of two (the verticl scle in the figures chnges ccording to the pek vlue). Detiled exmintion of Fig. 4 shows the presence of secondry density pek t the front of the em (position #5) which is displced downwrds (i.e. in the negtive x-direction). This corresponds to the front erosion discussed in the simplified model of Section nd is lso pprent t the front in Fig. 3. The erosion of the em front provides the momentum tht lnces the diversion of the flow of the mient mgnetoplsm in the positive x-direction. The erosion rte cn e computed quntittively y resorting to Figs. nd 4, nd exmining the temporl evolution of the density of the em front t dignostic loction 5. The sttionry mgnetic field structure, which cuses the flow diversion, is shown in the form of isomgnetic contours AB(x,z), i.e. the difference etween B(x, z) nd the initil homogeneous B o, in Figs. 5,. Notice the compression of the mgnetic field t the front followed y dimgnetic cvity t the ck. As descried in Section, for A < Ro the MIN x 1' 1 G MAX. = 6.5 x 1 - G INC. x 3.3 x 1 - G MIN. = MAX. = 1. x 11 8/CM CUT LOCATIONS IN Z 111 CMI x 1-1 G MAX. = 7.5 x 1 - G INC. = 3.7 x 1, G TIME = x 1-3 SECONDS MIN. MAX x 11 A/CM 1 O CUT LOCATIONS IN Z 111 CMI Fig. 4. Verticl em density profiles t the dignostic loctions for run #1. () At t = 1.5 msec. () At t =.5 msec. Fig. 5. Isomgnetic contours AB for run #1. (Solid lines represent compression of the mgnetic field over the mient, while dotted lines represent mgnetic field depression). () At t = 1.5 msec. () At t =.5 msec.

6 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol QUASINEUTRAL BEAM PROPAGATION TIME x 1-3 SECONDS TIME = x 1-3 SECONDS MIN. = MAX. 1. x 14 6/CM MIN. - MAX. 1.1 x 14 E/CM7 CUT LOCATIONS IN X DO. CMI 9 CUT LOCATIONS IN X (1 5 CM) S 6, 4 - MIN. = -1. x 1 7 CM/SEC MAX. = 1.7 x 15 CM/SEC - MIN x 17 CM/SEC MAX. = 3.4 x 15 CM/SEC S DIRECTION 11 5 CM) CUT LOCATIONS IN X 118 Fig. 6. Horizontl profiles of the em density () nd lterl velocity () for run #1 t t = 1.5 msec. 4-6 O -lox _1-1" ' 9. -DIRECTION 115 CMI Fig. 7. Sme s Fig. 6 t t =.5 msec. CUT LOCATIONS IN X 11, CMI 1 9 compression level sturtes t the vlue of AB/B necessry to divert the incoming plsm ions sidewys to the point tht they do not penetrte into the em. It should e noted tht the mgnetic field structure, which ws set up s erly s Sli; 1, remined essentilly sttionry over the length of the simultions. To understnd the phenomenology controlling the scling of the llistic propgtion time scle, we exmine the evolution of the horizontl em density profile (Figs. 6, 7) nd lterl drift velocity (Figs. 6, 7) t the center cut (loction #3, representing the mximum of the em density nd momentum flux) t times 1.5 nd.5 msec. A comprison of Figs. 3, 6 nd 7 in conjunction with Figs. 4, shows tht the em density hs een compressed t the center point, while the longitudinl length is preserved. Furthermore Figs. 6 nd 7 demonstrte tht the center of the em follows llistic trjectory (i.e. u x = ) except t the front nd the rer. The front of the em is eroding t downwrd velocity which hs sturted t vlue u x 1 7 cm/sec. As cn e seen y exmining the horizontl downwrd velocity profile t loction #3 in Figs. 6 nd 7, the erosion is penetrting ckwrds towrds the em center. Let us finlly exmine the flow ehvior of the mient plsm. Figures 8, show the flow speed t t = 1.5 nd Xi S e 15 O PLASMA VELOCITY PROFILES TIME X 1 - ' SECONDS OA 11 I I I ih\ RECTION (15 CMI MIN. = -3.8 x 14 CM/SEC MAX..3 x 17 CM/SEC CUT LOCATIONS IN X 4 CMI 1.87 MIN x 14 CM/SEC MAX. = 3.6 = 17 CM/SEC CUT LOCATIONS IN X 11 4 CMI Fig. 8. Horizontl profile of the mient plsm lterl velocity profiles for run #1. () At t = 1.5 msec. () At t =.5 msec.

7 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol. 53 PAPADOPOULOS ET AL msec t the horizontl cuts. It cn e seen tht the plsm is diverted upwrds t the front with n incresing speed, reching vlue of out x 1 7 cm/sec towrds the em center. This implies tht if we strted with em penetrted y mient plsm, the mient plsm ions nd their neutrlizing electrons will move outside the em. Since, s cn e seen in Fig. 8, there is no upwrd plsm flow from elow (i.e. cut #1) towrd the em center, the plsm density inside the em center will e reduced until there is no more plsm in the em. This of course will occur only if the front erosion time scle is longer thn the plsm evcution time. We will return to this point lter. TIME = x 1-3 SECONDS MIN. = MAX. = 1.8 x 14 9/CM, CUT LOCATIONS IN X 115 CMI Scling Considertions MIN. = -3.4 x 1, CM/SEC MAX. = 1.1 x 14 CM/SEC The previous discussion identified two criticl issues which control the scling of llistic em propgtion. The first refers to the scling of the downwrd drift of the em center (i.e. position t the intersection of horizontl nd verticl cuts #3) nd the upwrd drift of the plsm. The second refers to the rte of front erosion. As long s the front hs not eroded, the em center will propgte long trjectory determined y the self-consistent electromgnetic fields t the center of the em or plsmoid. CUT LOCATIONS IN X 11 5 CMI DIRECTION 115 CMI Fig. 1. Sme s Fig. 9 t t =.5 msec. z -1 o l!c) ! 7! 13 9! -DIRECTION 115 CMI MIN. = MAX. = 1. x 16 CCM 7 CUT LOCATIONS IN X 115 CM) 43 MIN. = -. x 1, CM/SEC MAX. =. x 15 CM/SEC CUT LOCATIONS IN X 115 CMI 4 Fig. 9. Horizontl profiles of the em density () nd lterl velocity () for run # t t = 1.5 msec. We exmine seprtely the scling with em velocity nd with em density. Runs #1-3 ll hve the sme numer of em prticles (4.8 x 1 18 ) or n equivlent n in. = 8, ut the flow velocity corresponds to 18, x 1 8, nd 4 x 18 cm/sec respectively. Figures 9, show the horizontl profiles of the em density nd downwrd displcement t time t=1.5 msec for run #. The center density profile nd center downwrd velocity re essentilly similr to run #1. However, the erosion speed t the front of cut #3 (Fig. 9) is lmost fctor of two fster thn in run #1 (i.e. x 1 7 cm/sec vs 1.1 x 1 7 cm/sec). This is confirmed y referring to the sme profiles t time t =.5 msec (Figs. 1, ). While there is still sustntil em density long the center cut #3 (Fig. 1), the front hs eroded to such n extent tht the em center is now drifting downwrds t speed of 1 7 cm/sec. In the ove two runs the erosion rte scles lmost linerly with u. The sme trend is evident from n exmintion of run #3 (u = 4 x 1 8 cm/sec). Figure 11 shows the density () nd downwrd em velocity () t n erlier time (t =.75 msec). While the density profile is similr to Figs. 6 nd 1 t t = 1.5 msec, the downwrd erosion speed is now 4 x 1 7 cm/sec, gin reveling liner scling with em velocity. As result of the fster erosion rte the profiles t t = 1.5 msec (Fig. 1) re

8 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol QUASINEUTRAL BEAM PROPAGATION MIN. = MAX. = 1. x 15 I/CM' CUT LOCATIONS IN X 116 CMI MIN. -4. x 11 CM/SEC MAX.= similr to the ones of run # t.5 msec (Fig. 11). By time t =.5 msec the em hs een displced nd modified sustntilly. However, it hs still mintined its plsmoid-like entity, lthough it is no longer following llistic propgtion pth (Fig. 13). Figure 13 shows AB contours t the sme time. They should e compred with the contours of the llistic propgtion mode (Fig. 5). Finlly, Figs. 14, show the plsm flow profiles t t = 1.5 msec for runs # nd #3. It cn e seen from these nd Fig. 9 tht, s expected from the previous results nd momentum conservtion, the diversion velocity of the plsm t the front s well s the outflow velocity of the plsm from the em center scle lmost linerly with u. It should e noted tht for the ove runs the L' W > -3 - x Z DIRECTION 115 CM) CUT LOCATIONS IN X 11 5 CMI Q Fig. 11. Sme s Fig. 1 for run #1 t t =.75 msec. S G MIN. = MAX. =.5 x 15 4/CM' INC. =.5 )4 1 7 X/CM. = MAX. = 1.7 x 15 ///CM 7 CUT LOCATIONS IN X 115 CMI MIN. =. x 1-1 G MAX. = 3.8 x 1-1 G INC x 1 -, G MIN. = -7.3 x 1 7 CM/SEC MAX. = S ".? CUT LOCATIONS IN X 11 5 CMI 7-8,, SO Z DIRECTION 11. CMI Fig. 1. Sme s Fig. 11 t t = 1.5 msec. Fig. 13. Isodensity () nd isomgnetic AB () contours for run #3 t t =.5 msec (solid lines represent compression while dshed lines represent depression of the mient mgnetic field).

9 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol. 53 PAPADOPOULOS ET AL. 157 TIME x 1-3 SECONDS MIN x 14 CM/SEC MAX x 1 1 CM/SEC MIN. MAX..5 x 11 /CM3 CUT LOCATIONS IN X 116 CMI CUT LOCATIONS IN X 114 CMI 6) 1 O 1.87 O MIN. = -4.6 x 16 CM/SEC MAX. = 8.3 x 1 1 CM/SEC MIN. = x 1 1 CM/SEC MAX. = CUT LOCATIONS IN X 11 6 CMI CUT LOCATIONS IN X 116 CMI is Fig. 14. Horizontl profile of the mient plsm lterl velocity t t = 1.5 msec. () For run #. () For run #3. vlue of the mgnetic field compression t the front lso scles linerly with u We next ddress scling issues relted to em-toplsm density rtios. Runs #1, 4 nd 5 ll hve the sme velocity u, = 18 cm/sec, ut the numer of em prticles is 4.8 x 1 18, 1. x 118 nd 3 x 1", corresponding to n /no oce. 8,, nd 5. Figures 15, nd 16, show horizontl profiles of em density nd lterl velocity for run #4 t t = 1.5 nd.5 msec. A comprison of Fig. 15 with Fig. 6 shows tht over the time scle of t = 1.5 msec (fi t = 4) the em density profiles re siclly self-similr for runs #1 nd 4. However, in the lower density cse (run #4), the center of the em drifts with ux = x 16 cm/sec while the front erosion speed is 1.7 x 1 7 cm/sec (Fig 15). In compring this with runs #1-3 (Figs. 6, 9, 11) we note tht for the high density cses there ws essentilly no drift of the center of the em efore erosion. The front erosion speeds, however, were 1 7, x 1' nd 4 x 1" cm/sec. Nmely, chnge in density y fctor of four resulted in 7% chnge in the front erosion rte. Referring to Fig. 16 we note tht while most of the energy density still remins t the em center, comintion of fster erosion rte nd DIRECTION 11 6 CMI Fig. 15. Horizontl profiles of the em density () nd lterl velocity () for run #4 t t = 1.5 msec CJ - 1 -!, TIME = x 1-3 SECONDS MIN. MAX. = 3.6 x 1 1 8iCM 6 CUT LOCATIONS IN X 116 CMI MIN. -.6 x 11 CM/SEC MAX. CUT LOCATIONS IN X I/O' CMI DIRECTION 116 CMI Fig. 16. Horizontl profiles of the em density () nd lterl velocity () for run #4 t t =.5 msec. 6 N) 1

10 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol QUASINEUTRAL BEAM PROPAGATION TIME = 1.5 x 1-3 SECONDS MIN. = -3.8 x 14 CM/SEC MAX. =. x 1 7 CM/SEC MIN. = MAX. 8.9 x 14 /t/cm3 CUT LOCATIONS IN X 115 CMI CUT LOCATIONS IN X 114 CMI MIN. = -5.3 x 14 CM/SEC MAX. = 4. x 1 7 CM/SEC MIN. = -.7 x 1 7 CM/SEC MAX. = CUT LOCATIONS IN X 114 CMI LI -16 o -18 >j CUT LOCATIONS IN X 114 CMI Z. DIRECTION 11. CMI Z DIRECTION 11. CMI Fig. 17. Horizontl profiles of the mient plsm lterl Fig. 18. Horizontl profiles of the em density () nd velocity for run #4 () t = 1.5 msec () t =.5 msec. lterl velocity () for run #5 t t = 1.5 msec. lrger downwrd displcement of the em center will destroy the llistic propgtion mode. Figures 17, show the velocity displcement profiles of the mient plsm t t = 1.5 nd.5 msec for run #4. Notice tht they re qulittively nd quntittively similr to the ones for run #1 (Figs. 8, ). Furthermore, the outflow shows constnt ccelertion. The ove sclings with density continue for the cse of run #5 (Figs. 18, ; 19, ), which hs fctor of four fewer em prticles thn run #4 nd sixteen times fewer thn run #1. It should finlly e noted tht for the ove runs the vlue of the mximum field compression ws pproximtely the sme. In summry, the simultions descried ove demonstrte tht the presence of propgting ion em with n no sets up n electrodynmic configurtion tht lterlly diverts the mient plsm in such fshion tht no penetrtion of the min em occurs. The lterl diversion speed scles linerly with the em velocity nd is independent of the em-to-plsm density rtio. Although specific simultion studies with vrious vlues of the mient mgnetic field B o were not performed, the physicl understnding dicttes liner scling of the lterl speed with B o. The em responds to this configurtion in mnner tht is consistent with conservtion of momentum in the plsm frme. As consequence of MIN. = MAX. = 9.6 x 1134 //CAP :UT LOCATIONS IN X 115 CMI 8 MIN. = -3.8 x 1, CM/SEC MAX. = CUT LOCATIONS IN X 115 CM) Fig. 19. Horizontl profiles of the em density () nd lterl velocity () for run #5 t t =.5 msec.

11 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol. 53 PAPADOPOULOS ET AL. 159 this, for time scles tht re shorter thn the front erosion time (i.e. for long thin ems) nd for nm >> nomo, the plsm is evcuted from the centrl em region with minimum em displcement. In fct, the simultions show tht the dynmics of the system re such tht focusing is produced t the center while momentum is lnced y shedding of surfce prticles from the em. The em will susequently follow llistic pth until erosion of the front destroys it. The erosion rte ws found to scle linerly with the em velocity nd y the previous rgument with B o, while it is inversely proportionl to (n /no) t the front. Time Scle for Bllistic Propgtion compression t the front. From conservtion of energy, o u = u where us is given from Eq. l s ui eb A A = U (1) Mo (i.e. the trnsverse energy equls the potentil drop). For u: < t4, i.e. A/Ro << 1, Eq. (9) ecomes u: = (u )(u + u (u u), (9) From the previous nlysis we cn derive the following so tht generl conclusions concerning the time scle for cross AB U field llistic propgtion of neutrlized ion em of tilt, = 11. (11) Bo width A nd length L with density n nd ion mss M. (i) The plsm will e evcuted from the em center The erosion rte is then found from Eqs. (8) nd t n verge rte given y (11) s where de.e. dtmo AB E, = u The evcution time scle r 1 for em of lterl width A is esily computed from Eqs. (4) nd (5) s 1 n L Mo nr > fi ri < ( A )h/. (6) no A Ro M During this time, the em displcement Ax t, is given y A X n M A n MO (7) For times greter thn r 1, no further displcement occurs until the em front is eroded. (ii) The front of the em cts s shield tht llows the ulk of the em to propgte s descried ove. The rte of em erosion cn e estimted y simple energy nd momentum considertions. The em erosion rte dz/dt is given y lncing momentum in the z-direction, i.e. dz nm = nomo (u u ) (8) dt where u is the mient plsm speed in the z- direction fter it hs een diverted y the mgnetic (4) (5) 1 dz nomo A AB n o Mo A = < ( 1) u t nmnm R. Notice tht for AIR. < 1 nd no Mo < nm the erosion rte is very smll frction of the em speed. For em of length L we cn define em erosion time s the time to penetrte to z = L/ from the front. Then Eq. (1) gives n erosion time scle r s (13) An lterntive interprettion of Eq. (1) pplies to the cse of constnt em injection. Under conditions such tht Ax /A << 1 s given y Eq. (8), Eq. (1) sttes tht em injected into mgnetoplsm with n injection rte fster thn the erosion rte will propgte llisticlly t ll times. Summry nd Conclusions We presented ove physicl model, supported y computer simultion studies, which demonstrted tht dense (nm >> nom ), thin (A/R < 1, A/ L << 1) neutrlized ion ems or plsmoids cn propgte llisticlly if injected in the ionosphere or mgnetosphere cross the mient mgnetic field. The results presented were sed on two-dimensionl hyrid simultions performed in the plne perpendiculr to the mgnetic field. We re in the process of performing three-dimensionl simultions s well s extending the simultions of the scling discussed ove to other M /M rtios, different vlues of

12 Geophysicl Monogrph Series Plsm Wves nd Instilities t Comets nd in Mgnetospheres Vol QUASINEUTRAL BEAM PROPAGATION B o nd other vlues of /Ro. These, long with specific pplictions to ctive experiments, plsmoid propgtion nd strophysicl jets, will e pulished elsewhere. Before closing we should remrk tht two-dimensionl simultions were lso performed with the mgnetic field in the simultion plne. Lterl diversion consistent with the erlier simultion results ws oserved. The only dditionl feture ws tht the field lines were slightly drped round the em s they drifted upwrds. As expected, the mode of em propgtion ws not ffected to ny oservle degree. Acknowledgements. The uthors re grteful to Drs. R. Sudn, T. Antonsen, P. Wheeler, nd J. Denvit for mny criticl comments nd suggestions during the course of this reserch. This work ws supported y the U.S. Deprtment of Energy under contrct numer DE-ACO3-85SF References Bker, D.A. nd J.E. Hmmel, Experimentl Studies of the Penetrtion of Plsm Strem into Trnsverse Mgnetic Field, Phys. Fluids 8, (1965). Birko, V.F. nd G.S. Kirchenko, Soy. Phys. Tech. Phys. 3, (1978). Crgill, P., S. Srm nd K. Ppdopoulos, Lower Hyrid Wves nd Their Consequences for Cometry Bowshocks, J. Geophys. Res. (communicted), Chpmn, S., Idelized Prolems of Plsm Dynmics Relting to Geomgnetic Storms, Rev. Mod. Phys. 3', (196). Chpmn, S. nd V.C.A. Ferrro, A New Theory of Mgnetic Storms, Terrestril Mgnetism nd Atmospheric Electricity 37, (1931). Ferrro, V.C.A., On the Theory of the First Phse of Geomgnetic Storm: A New Illustrtive Clcultion Bsed on n Idelized (Plne not Cylindricl) Model Field Distriution, J. Geophys. Res. 57, (195). Mnkofsky, A., R.N. Sudn, nd J. Denvit, J. Comp. Phys. 7, 89 (1987). Ppdopoulos, K., A. Mnkofsky nd A. Droot, Phys. Rev. Lett. 61, 94 (1988). Peter, W. nd N. Rostoker, Phys. Fluids 5, 73 (198). Schmidt, G., Plsm Motion Across Mgnetic Fields, Phys. Fluids 3, (196). Scholer M., On the Motion of Artificil Ion Clouds in the Mgnetosphere, Plnet. Spce Sc. 18, 977, Shnhn, W. (unpulished), Tuck, J.L., Plsm Jet Piercing of Mgnetic Fields nd Entropy Trpping in Conservtive System, Phys. Rev. Lett. 3, (1959).